A dynamic four-state system is considered within the context of multistate Landau-Zener theory. It is shown that the theory accounts very well for the time-dependent state populations and final transition probabilities even in cases when multiple crossings appear in close vicinity of each other. This is also true for multiple paths systems when the phases are appropriately accounted for. It is found that transitions may take place also between diabatic states that do not couple directly and that the dynamics of such crossings may be accurately described within the multichannel Landau-Zener theory.

Recently, integrability conditions (ICs) in mutistate Landau-Zener (MLZ) theory were proposed. They describe common properties of all known solved systems with linearly time-dependent Hamiltonians. Here we show that ICs enable efficient computer assisted search for new solvable MLZ models that span complexity range from several interacting states to mesoscopic systems with many-body dynamics and combinatorially large phase space. This diversity suggests that nontrivial solvable MLZ models are numerous. Additionally, we refine the formulation of ICs and extend the class of solvable systems to models with points of multiple diabatic level crossing.